Type Ia supernovae are thought to result from a thermonuclear explosion of an accreting white dwarf in a binary system1,2, but little is known of the precise nature of the companion star and the physical properties of the progenitor system. There are two classes of models1,3: double-degenerate (involving two white dwarfs in a close binary system2,4) and single-degenerate models5,6. In the latter, the primary white dwarf accretes material from a secondary companion until conditions are such that carbon ignites, at a mass of 1.38 times the mass of the Sun. The type Ia supernova SN 2011fe was recently detected in a nearby galaxy7. Here we report an analysis of archival images of the location of SN 2011fe. The luminosity of the progenitor system (especially the companion star) is 10–100 times fainter than previous limits on other type Ia supernova progenitor systems8,9,10, allowing us to rule out luminous red giants and almost all helium stars as the mass-donating companion to the exploding white dwarf.